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Following the recent report of superconductivity in the bilayer nickelateLa$_{3}$Ni$_{2}$O$_{7}$ under pressure, we present an analysis of theelectronic and magnetic properties of La$_{3}$Ni$_{2}$O$_{7}$ as a function ofpressure using correlated density functional theory methods (DFT+$U$). At thebare DFT level, the electronic structure of the ambient and high-pressure phaseof La$_{3}$Ni$_{2}$O$_{7}$ is qualitatively similar. Upon including localcorrelation effects within DFT+$U$ and allowing for magnetic ordering, we finda delicate interplay between pressure and electronic correlations. Within thepressure-correlations phase space, we identify a region (at $U$ valuesconsistent with constrained RPA calculations) characterized by a spin-statetransition with increasing pressure, where the ground state ofLa$_{3}$Ni$_{2}$O$_{7}$ changes from a high-spin A-type antiferromagnet to alow-spin G-type antiferromagnet with contrasting electronic structures. Whilethe energy landscape of this material is rich, with many competing magneticstates, we find a common thread to be that all of these different states aredriven by the Ni-$d_{x^{2}-y^{2}}$ orbitals.

Electronic structure and magnetic properties of La$_{3}$Ni$_{2}$O$_{7}$ under pressure